Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, April 06, 2006, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Sofya Raskhodnikova (Weizmann Institute of Science)

Sublinear Algorithms for String Compressibility and the Distribution Support Size

Imagine having to choose between a few compression schemes to compress a very long file. Before deciding on the scheme, you might want to obtain a rough estimate on how well each scheme performs on your file. We consider the question of approximating compressibility of a string with respect to a fixed compression scheme, in sublinear time.

In the talk, we will concentrate on the run-length encoding and a version of Lempel-Ziv as our example compression schemes. We present algorithms and lower bounds for approximating compressibility with respect to both schemes. We show that compressibility with respect to Lempel-Ziv is related to approximating the support size of a distribution. This problem has been considered under different guises in the literature. We prove a lower bound for it, at the heart of which is a construction of two positive integer random variables, X and Y, with very different expectations and the following condition on the moments up to k:
E[X]/E[Y] = E[X²]/E[Y²] = ... = E[X^k]/E[Y^k].

Joint work with Dana Ron, Ronitt Rubinfeld, Amir Shpilka and Adam Smith.

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